Question: $86$ people attended a baseball game. Everyone there was a fan of either the home team or the away team. The number of home team fans was $49$ less than $2$ times the number of away team fans. How many home team and away team fans attended the game?
Answer: Let $x$ equal the number of home team fans and $y$ equal the number of away team fans. The system of equations is then: ${x+y = 86}$ ${x = 2y-49}$ Solve for $x$ and $y$ using substitution. Since $x$ has already been solved for, substitute ${2y-49}$ for $x$ in the first equation. ${(2y-49)}{+ y = 86}$ Simplify and solve for $y$ $ 2y-49 + y = 86 $ $ 3y-49 = 86 $ $ 3y = 135 $ $ y = \dfrac{135}{3} $ ${y = 45}$ Now that you know ${y = 45}$ , plug it back into ${x = 2y-49}$ to find $x$ ${x = 2}{(45)}{ - 49}$ $x = 90 - 49$ ${x = 41}$ You can also plug ${y = 45}$ into ${x+y = 86}$ and get the same answer for $x$ ${x + }{(45)}{= 86}$ ${x = 41}$ There were $41$ home team fans and $45$ away team fans.